Another pertinent link with the past is that Harding's final trumpet performance came in a NYO Prom that featured Mahler's second symphony, the work he will conduct with the SRSO. "Mahler has been an obsession since Chetham's [music school in Manchester], where my circle of friends were the nerds in a school full of nerds," he recalls. "For us it was all about the Germanic repertoire, and back then we were very snooty about English or French music. Music is not unlike football in that sense: it's probably healthy to be obsessed and judgmental at some stage. Of course I've learned to love other types of music, but Mahler has always been a constant and it has been amazing to see how much he is now played. I was once given a 1906 Grove Dictionary, which essentially said he was a pretty good conductor but a mediocre composer. And although he did rightly predict that 'my time will come', he surely never envisaged this level of popularity. It's almost dangerous."

Harding's early conducting career is one of the most remarkable of modern times. He was just 19 when he was given the chance to conduct the City of Birmingham Symphony Orchestra by his mentor, Simon Rattle. By 21 he had conducted the Berlin Philharmonic and at the same age became the youngest conductor in Proms history. At 22 he was working with Peter Brook on a production of Don Giovanni, and he first appeared at Covent Garden when he was 23.

"At the time I didn't quite realise how significant all this was. It was just very exciting. At the beginning, until I was about 30 really, everything came so fast and easily." But while he has continued to work on a stream of A-list projects – being the first Briton to open a season at La Scala, cementing his long-term relationship with the London Symphony Orchestra as their principal guest conductor, running his own orchestras in Scandinavia and Germany – there has also been a feeling that his career has not carried on with the same momentum. As one headline put it: "Prodigy Ages into a Merely Young Conductor" and for the first time Harding needed a plan, part of which was his move to Stockholm.

"At some point you have to get into a cocoon and metamorphose from an interesting young talent into a proper conductor. And you soon realise that you really have to work hard at becoming a butterfly." Having spent most of the previous 12 years working with chamber orchestras it was important for Harding to run a symphony orchestra, and so he looked for one that was "good enough that I would really enjoy it, but also somewhere I could make a difference. I wanted us to raise each other, and I think it's working."

Indeed the critical response to his work with the SRSO has been increasingly positive, and he has also instigated extra-musical activities such as a forthcoming series of lectures by artists, academics, scientists and philosophers pegged to concerts. Examples include Marcus du Sautoy on the connections between music and mathematics in Mozart, Berg and Messiaen, and Philippe Sands on the relationship between human rights and the music of Bach, Zimmermann and others.

Harding also gives pre-concert talks. "People love to know what you are thinking and to feel included." For a conductor who used to be characterised as intense and, as one observer put it, was "acquiring a reputation as a young man who knew best", at rehearsals in Stockholm he now cuts a relaxed figure, laughing with the orchestra when requesting quieter playing to allow a woodwind line to emerge: "If this poor guy is going to spend his life figuring out this music, we need to hear the melody." It is all delivered in the indeterminate mittel-European tones of someone who has spent most of his adult life speaking to people for whom English is not their first language. "It goes with the territory," he says, "although when speaking to my parents, or watching football," – he is a Manchester United season ticket holder – "it pretty quickly slips back where it used to be."

Harding was born in Oxford in 1975. His father was a metallurgist at the university and his mother an administrator in the engineering department. Both were keen amateur musicians, and other musical links include an uncle who played in the Hallé Orchestra under Barbirolli, and a maternal grandmother who was friends with Imogen Holst and knew Vaughan Williams, who "once kissed her, unbidden, in a taxi".

He exhibited an early aptitude for music but had to wait until he was eight, "and I got some strong front teeth", to play the trumpet, which led on to his moving from his Oxford comprehensive school to Chetham's. Soon after he won a place in the NYO, which led to his Proms debut in 1989, but he says that while he "did very well" with the trumpet until he was 14 or 15, "you can only get so far with talent and then you need hard work as well. At about that point other people shot ahead."

By this stage Harding's interest had moved towards conducting, but he retained his place in the NYO "beyond the time when I really should have been replaced. But I was working with Simon and conducting, and they knew it was good for me to sit in rehearsals with these wonderful conductors as part of an orchestra. So they kind of turned a blind eye to the fact that I hadn't practised the trumpet in four years, and I was very grateful for that."

The Rattle link came when Harding was 17 and conducted a student performance of Schoenberg's Pierrot Lunaire. A teacher sent a recording to Rattle, who was so impressed that he offered Harding a job as an assistant. Eighteen months later Harding conducted the CBSO in a Bartók suite in Birmingham's Symphony Hall. "And that was the beginning of everything," he says. "I was very grateful to my parents for not being pushy as so many musical parents are, but in effect Simon Rattle came along and did that for them."

Harding then won a place at Cambridge to study music but left after a year. "In reality I was probably there for about six weeks." He had received an offer from Claudio Abbado – who called him "my little genius" – to become an assistant at the Berlin Philharmonic. "And as my early Mahler obsession went along with a hero worship of Abbado, who I thought was the greatest Mahler conductor, I was never going to say no."

What was it like to conduct the Berlin Philharmonic as a 21-year-old? "In all those early concerts I was probably a pretty dreadful conductor, but I was full of promise and energy, and I was lucky that people could see the good things despite a lot of distractions. And I was Rattle's protege. His word counts for a lot. When he turned up as a 20-year-old people thought it was ridiculous, and 20 years later they regretted saying that, so I was offered a lot of chances. But I like the fact that I can look back at my mistakes and still say that I made them for the right reasons." He points to a Don Giovanni recording he made when he was 23. "I would never do it like that now, but any mistakes were all mine because I read it that way and had not simply listened to Giulini's recording and tried to copy it. What would be the point of that? There is an audacity in youth that you would like to recapture."

Harding also says that several of the institutions he worked with were unprepared for such a young maestro. "Telling a young person to be more patient or trusting or relaxed is pointless. It is like telling Wayne Rooney to score more goals. He will score as many goals as he is able. He is trying. These things will come when you find a way to do them. There was the odd orchestra where I was a bit impetuous, but a 19-year-old is going to be a 19-year-old, why fight back at that? One reason I have had such a good and long relationship with the LSO – and I did have some really hard times – was that they were always above hitting back. After going through a divorce" – he has two children with viola player Béatrice Muthelet and still lives near them in Paris – "and a period of being quite upset with the world, people made a point of coming up to me and saying how glad they were that I seemed happier because so many of them had been there."

The period of domestic and professional turbulence coincided with Harding being "nowhere near an eminence grise, but no longer the new kid on the block. I always knew that between 30 and 50 are probably the most important years you have as a conductor, and I am now older than Simon was when I met him. That's slightly terrifying, and so my work in Stockholm has been among the most important I have done."

As well as conducting the SRSO he watched them work under other conductors. "I knew this was an orchestra of incredible refinement and talent, but I also thought someone should just take the lid off, and that was something I thought I could do." During the last seven years he has made a series of key appointments, as well as let people go. "That's an important part of the job, too. At the beginning the orchestra were desperate to make more recordings and tour, but I wanted to wait a little. Now I'm very impatient to share what this orchestra does as widely as possible."

Their Prom will be his second appearance in the last two years after a decade away. "I realised just how much I missed it. There is not much about the Albert Hall that is right, but the Proms is an astonishing festival where you can sense how much the audience really want to hear the music. There are all sorts of reasons why we get hung up on comparing performances, but we sometimes forget that music is not about point scoring, it is about sharing something, and at the Proms you can just wallow in this incredible repertoire we have. After all this time, and all the work we've done, I was delighted to be able to bring this orchestra to London. I really can't wait."

• Prom 57: Mahler Symphony No 2 Resurrection is at the Royal Albert Hall, London SW7, and broadcast live on Radio 3 on 29 August. bbc.co.uk/proms.